# Determine The Value Of a So That When P(x) = (a^2)(x^3)-3ax+1 Is Divided By x-2 There Is No Remainder. Help, Please?

Mar 2, 2018

when divided by $x - 2$, there is no remainder, hence $x = 2$ is the solution.

That is, when you plug in $x = 2$ in a^2x^3−3ax+1, it would be equal to 0.

2^3a^2 −3(2)a+1=0

8a^2 −6a+1=0

8a^2 −4a -2a+1=0

4a(2a −1) -1(2a-1)=0

$\left(4 a - 1\right) \left(2 a - 1\right) = 0$

Therefore, $a = \frac{1}{2} \mathmr{and} \frac{1}{4}$